7,747 research outputs found
A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking
In this paper, a new chaotic pseudo-random number generator (PRNG) is
proposed. It combines the well-known ISAAC and XORshift generators with chaotic
iterations. This PRNG possesses important properties of topological chaos and
can successfully pass NIST and TestU01 batteries of tests. This makes our
generator suitable for information security applications like cryptography. As
an illustrative example, an application in the field of watermarking is
presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information
Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211,
October 201
Higher order Dependency of Chaotic Maps
Some higher-order statistical dependency aspects
of chaotic maps are presented. The autocorrelation
function (ACF) of the mean-adjusted squares, termed the
quadratic autocorrelation function, is used to access nonlinear
dependence of the maps under consideration. A simple
analytical expression for the quadratic ACF has been
found in the case of fully stretching piece-wise linear maps.
A minimum bit energy criterion from chaos communications
is used to motivate choosing maps with strong negative
quadratic autocorrelation. A particular map in this
class, a so-called deformed circular map, is derived which
performs better than other well-known chaotic maps when
used for spreading sequences in chaotic shift-key communication
systems
Compression and diffusion: a joint approach to detect complexity
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular
research tool among physicists, especially when applied to a dynamical system
fitting the conditions of validity of the Pesin theorem. The study of time
series that are a manifestation of system dynamics whose rules are either
unknown or too complex for a mathematical treatment, is still a challenge since
the KS entropy is not computable, in general, in that case. Here we present a
plan of action based on the joint action of two procedures, both related to the
KS entropy, but compatible with computer implementation through fast and
efficient programs. The former procedure, called Compression Algorithm
Sensitive To Regularity (CASToRe), establishes the amount of order by the
numerical evaluation of algorithmic compressibility. The latter, called Complex
Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA),
establishes the complexity degree through the numerical evaluation of the
strength of an anomalous effect. This is the departure, of the diffusion
process generated by the observed fluctuations, from ordinary Brownian motion.
The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov
complexity. This makes both algorithms especially suitable to study the
transition from dynamics to thermodynamics, and the case of non-stationary time
series as well. The benefit of the joint action of these two methods is proven
by the analysis of artificial sequences with the same main properties as the
real time series to which the joint use of these two methods will be applied in
future research work.Comment: 27 pages, 9 figure
Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems
Traditionally, chaotic systems are built on the domain of infinite precision
in mathematics. However, the quantization is inevitable for any digital
devices, which causes dynamical degradation. To cope with this problem, many
methods were proposed, such as perturbing chaotic states and cascading multiple
chaotic systems. This paper aims at developing a novel methodology to design
the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite
precision. The proposed system is based on the chaos generation strategy
controlled by random sequences. It is proven to satisfy the Devaney's
definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The
application of HDDCS in image encryption is demonstrated via FPGA platform. As
each operation of HDDCS is executed in the same fixed precision, no
quantization loss occurs. Therefore, it provides a perfect solution to the
dynamical degradation of digital chaos.Comment: 12 page
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